Analytical solution of one dimensional time fractional Black-Scholes equation through Laplace adomian decomposition method

Abstract

This article is aimed at solving the one dimensional fractional order Black-Scholes equation to investigate the dynamics of option derivatives. The method used to solve this problem is a modified decomposition method. The fractional order derivatives are given in the form of Caputo operator. The behavior of European options is well described by their analytical solutions. In this paper, the analytical solution of European option pricing problem is obtained through Laplace Adomian decomposition method (LADM). The LADM solution is compared to the exact solution and the solution graphs show a close contact between the LADM and exact solution. Moreover, it is shown that the solutions of fractional Black-Scholes equations converge to the solutions of integer order, thereby proving that LADM is an efficient technique to solve fractional order partial differential equations.